Surface triggered stabilization of metastable charge-ordered phase in SrTiO3

Charge ordering (CO), characterized by a periodic modulation of electron density and lattice distortion, has been a fundamental topic in condensed matter physics, serving as a potential platform for inducing novel functional properties. The charge-ordered phase is known to occur in a doped system with high d-electron occupancy, rather than low occupancy. Here, we report the realization of the charge-ordered phase in electron-doped (100) SrTiO3 epitaxial thin films that have the lowest d-electron occupancy i.e., d1-d0. Theoretical calculation predicts the presence of a metastable CO state in the bulk state of electron-doped SrTiO3. Atomic scale analysis reveals that (100) surface distortion favors electron-lattice coupling for the charge-ordered state, and triggering the stabilization of the CO phase from a correlated metal state. This stabilization extends up to six unit cells from the top surface to the interior. Our approach offers an insight into the means of stabilizing a new phase of matter, extending CO phase to the lowest electron occupancy and encompassing a wide range of 3d transition metal oxides.


Supplementary Note 1: DFT calculation and symmetry analysis of the bulk LSTO
We investigate the atomic and electronic structures of the bulk La0.25Sr0.75TiO3(LSTO) using the density functional theory (DFT) with semi-empirical Hubbard U correction.
Considering the experimentally observed oxygen octahedral rotation pattern 1,2 , we assume bulk LSTO has a 0 a 0 c -Glazer`s notation.We optimize the lattice constants and the internal atomic coordination of metallic bulk LSTO based on the 2a × 2a × 2c cell.The optimized in-plane and out-of-plane lattice constants with the anti-phase octahedral rotation distortion (a 0 a 0 c -in Glazer's notation) are a = 0.39679 and c = 0.40159 nm, respectively.For the LaSr doping configuration, we investigate several doping configurations, and the total energy difference between different doping configurations is up to 3 meV/formula unit.A configuration where LaSr dopants are linearly aligned along the out-of-plane direction is found to be energetically favorable, and this doping configuration is adopted for all the calculations.It was theoretically shown that breathing oxygen octahedral distortion, which expands or contracts the oxygen octahedra nearest neighbor unit cells, allows charge ordering (CO) in half-doped titanate double perovskite 3 .Therefore, we initially introduce periodic modulation of oxygen octahedral distortion that consists of expansion and contraction of TiO6 octahedra and obtained the charge-ordered LSTO bulk structure.It shows the antiferromagnetic Mott insulating behavior with the localized Ti 3d band as shown in Supplementary Figure 1.The optimized lattice constants of this structure obtained from the 2a × 2b × 4c cell (Supplementary Fig. 2a) are a = 0.39869, b = 0.39506, and c = 0.40371 nm, respectively.We analyze the lattice modulation of the CO state bulk LSTO.The lattice modulations of the CO state bulk LSTO are decomposed into distortion modes, i.e., ∆r = ∑i ci Φi, where ∆r is the lattice modulation vector of the bulk LSTO as the atomic displacement vector from the symmetrical structure (Supplementary Fig. 2b), ci is the coefficients of the normalized distortion mode Φi (i = 1, 2, 3, z-and rem), respectively.For the distortion mode vector Φi (i = 1, 2, 3, z-and rem), Φ1 is the inter-layer breathing mode that is oxygen octahedra volume expansion and contraction along the z direction (Fig. 1c).Φ2 is the intra-layer breathing mode that an in-plane nearest-neighbor oxygen octahedron to either expand or contract.This expansion and contraction of oxygen octahedra along the in-plane direction have a one-layer interval and out-of-phase motions along the z direction (Fig. 1d).Φ3 is the Jahn-Teller type distortion mode which has different Ti-O bond lengths along the x and y directions.Similar to Φ2, Φ3 also has a one-layer interval and out-of-phase motions along the z direction (Fig. 1e).
Φz-is the antiferrodistortive rotation (a 0 a 0 c -in Glazer's notation) i.e., an anti-phase octahedral rotation along the z direction (Fig. 1f).Note that these distortion mode vectors Φi (i = 1, 2, 3, z-), are orthogonal to each other.The remaining term (Φrem) mainly comes from the displacements of atoms near the LaSr dopants (Supplementary Fig. 3).dis are oxygen displacement with respect to the high symmetric structure, which is defined as the multiply ci by individual oxygen displacement of the normalized distortion mode vector Φi (i = 1, 2, 3, z-).

Supplementary Fig. 1 | Spin-polarized DOS of the charge-ordered insulating bulk LSTO.
Total DOS is represented by black lines, and those projected onto the Ti 3d and O 2p orbitals are represented by blue and red lines, respectively.Positive and negative regions correspond to the up-spin and the down-spin states, respectively.The midpoint between the energies of the lowest unoccupied state and the highest occupied state is set to be zero and represented by the vertical line.Supplementary Fig. 2 | Atomic structure of the LSTO bulk.a Charge-ordered metastable structure of the LSTO bulk.The obtained structure shows the periodic expansion and contraction of the oxygen octahedral pattern.b Symmetric structure of the LSTO bulk without periodic structural distortion.In a, b the linear configuration of the LaSr dopant in the 2a × 2b × 4c cell is adopted for both structures.The unit cell is represented by black lines.Purple, chartreuse, red, blue, yellow, and white spheres represent the Sr, La, and O atoms and Ti 4+ , Ti 3+ , and partially filled Ti (4-δ)+ cations, respectively.In a the yellow shades on the Ti 3+ O6 octahedral surface are guides for eyes.

Supplementary Note 5: Optical conductivity measurements
To obtain the complex optical conductivity spectra  ̃()[≡  1 () +  2 ()] , we performed ellipsometry at room temperature which directly yields the complex optical constants without Kramers-Kronig analysis.We measured the ellipsometric angular spectra of the superlattices using a spectroscopic ellipsometer (VASE, J. A. Woollan).The angles of the incident light and the spectral ranges were 65°, 70°, and 75° (angle between the plane of the samples and the incident beam), and 0. The incoherent mode near 1.3 eV, observed in our LSTO films (Fig. 2e), was not present at the SrTiO3 substrate (Supplementary Fig. 7).This implies that the incoherent spectral peaks are the intrinsic behavior of the LSTO films.In the high energy region σ1(ω) of LSTO, similarly to the case of undoped STO, a strong absorption above 4 eV is observed due to the charge transfer excitation (CTE) from O 2p to Ti t2g bands, as shown in Supplementary Figure 7.We note that the CTE edge of the LSTO spectra shifts to higher energies compared with that of an undoped STO single crystal, which has been observed for the doped STO bulk samples 8 .
Notably, the La ion doping leads to the emergence of spectral weight below CTE.
To determine an optical gap, we extracted an onset energy (EOnset) of optical conductivity spectra.Extrapolating the low energy shoulder of the incoherent mode peak near 1.3 eV of semiconducting 6 u.c.thick LSTO film (Supplementary Fig. 8), we obtained the onset energy (EOnset) of 600 meV.In the small polaron system, the optical gap is regarded as twice the polaron binding energy (Ep) due to the two relaxation channels which can lead to the hopping transfer or on-site relaxation 5,7 .The activation energy (EA) is related to the polaron binding energy (Ep) and electron transfer integral (J).The transfer integral (J) is determined by tunneling process, thus depends on the wavefunction overlap or orbital overlap between adjacent sites.In addition, intersite Coulomb repulsion (EC) should be considered especially in highly doped systems since it disturbs electron hopping process 5,9 .The relationship of EA, EP, J, and EC in the SPH model can be expressed as 5 : Supplementary Fig. 7 | Optical conductivity spectra of STO substrate.Optical conductivity is obtained from the ellipsometry of the STO substrate.Note that no incoherent part of the spectra is observed.

Supplementary Note 6: Coherent Bragg rod analysis
Experimentally recorded CTR data were first background subtracted using the 2D detector images, and then properly corrected for geometric and polarization factors.The resulting structural factors were used for the subsequent COBRA analysis.The total 3D electron densities (EDs) for the complete atomic structures of the thin film system, including the epitaxial thin film unit cells and the top few unit cells of the substrate (e.g.typically 6-8 substrate unit cells), were reconstructed from the complete set of CTRs by using a Fourier phase retrieval iterative technique, known as coherent Bragg rods analysis (COBRA), through a self-developed MATLAB code universally optimized for systems with symmetry lower than 4 mm (or a simple four-fold symmetric system).Within each iteration in COBRA analysis, real space and reciprocal space constraints are alternatively applied to recover the phase information at each reciprocal space point from measured CTRs.In the cases where thin film and substrate symmetries are different (i.e., different octahedral rotation patterns and amplitudes), the epitaxial thin film may form different structural domains (as compared to the bulk substrate).In this case, the reconstructed thin film ED contains thin film structural information that is folded into the substrate-defined in-plane unit cell.Specific information such as oxygen octahedral rotation can be deduced from the broadening of the folded-unit cell ED profile induced by the rotation.
The general approach for obtaining experimental errors based on traditional fitting models is not applicable to COBRA-generated Eds.A method called "Noise Analysis", based on bootstrap-type statistical analysis was used to determine the uncertainties in COBRA results.
This method applies additional random noises to the experimentally obtained CTR data and then analyzes the degree of scattering in the parameters extracted from EDs.
Supplementary Fig. 9 | Definition for the height of oxygen octahedron.The atomic structure of the LSTO is shown.Green, white, and red spheres represent (La, Sr), Ti, and O atoms, respectively.The apical oxygen-to-oxygen distance (OApi.-OApi.) is defined as described above figure, which is used for quantitative analysis of the octahedral modulation in this study.

Supplementary Note 7: STEM/ EELS analyses
EELS 2D scan was conducted across the LSTO/STO interface to trace the electron confinement at Ti 3d orbitals.When an additional electron is confined at the Ti 3d orbital, it tends to occupy the t2g orbital which is at a lower energy state due to the crystal field splitting.
If the t2g orbital is occupied, the fine structure of EELS Ti-L2,3 edge is changed in such a way that the t2g peak becomes suppressed compared to the eg peak as fewer core electrons are excited to t2g and the Ti-L2,3 edge shifts to lower energy (redshift) as the binding energy is lowered.We quantified the Ti 3+ fraction by using multiple linear least square (MLLS) fitting of the EELS Ti-L2,3 edge with the assumption that it consists of a linear combination of the signals from the Ti 4+ and Ti 3+ state.The periodic fluctuation in the Ti 3+ fraction is clearly captured when the measured Ti 3+ fraction is plotted with the distance from the interface (Fig. 3d).However, it should be mentioned that the measured Ti 3+ profile can be spread out from the real profile because the EELS signal can also be generated from neighboring atomic sites by beam spreading and channeling.
structure, the dipole correction was used in the z-direction to alleviate the unintended external electric field resulting from the image supercell.
We also investigate the magnetic and electronic structures of the LSTO/STO slab.We consider several different magnetic configurations, and the total energy difference between different magnetic configurations is up to 6.5 meV.We find an A-type-like antiferromagnetic (AFM) spin alignment as the ground-state magnetic structure of the LSTO thin films for all t investigated, where Ti 3+ has parallel spin alignment in the in-plane direction, and anti-parallel spin alignment in the out-of-plane direction (Fig. 4d, Supplementary Fig. 16b, Supplementary Fig. 17c, f and Supplementary Fig. 18c).We would like to note that the obtained magnetic state of the LSTO film, the A-type-like AFM order, is different from those of other rare-earth titanates with a -a -c + rotation pattern which has G-type AFM or ferromagnetic (FM) 4 order (a - a -c + Glazer's notation).The A-type-like AFM order can be stabilized by the a 0 a 0 c -rotation by super-exchange interaction 11,12 .We also calculate the electronic band structure and the density of states of the LSTO/STO slab as shown in Supplementary Figure 13 and Figure 4a.The slab is insulating when t ≤ 6 u.c., while metallic when t = 8 u.c..
We analyze the lattice modulation of the LSTO film similar to the bulk LSTO.The lattice modulations of the LSTO films are decomposed into distortion modes, i.e., ∆r t = ∑i c t i Φ t i, where ∆r t is the lattice modulation vector of the LSTO film with the thickness t (t = 2, 4, 6, and 8 u.c.) defined as the atomic displacement vector from the symmetrical structure, c t i is the coefficients of the normalized distortion mode Φ t i (i = 1, 2, 3, z-and rem) with Φ t 1: the interlayer breathing mode, Φ t 2: the intra-layer breathing mode, and Φ t 3: the Jahn-Teller type distortion mode, Φ t z-: the antiferrodistortive rotation (Supplementary Fig. 14).For t = 8 u.c., ∆r 8u.c. and Φ 8u.c i are defined for only the modulated LSTO (top 6 layers, 0 th to -5 th layers), i.e., the atomic displacements of the -6 th and -7 th layers are excluded in the definition of ∆r 8u.c. and Φ 8u.c i. d t is are oxygen displacements with respect to the high symmetric structures, which are defined as the multiply c t is by individual oxygen displacements of the normalized distortion mode vectors Φ t is (i = 1, 2, 3, z-).Oxygen octahedral rotation angles θ t z-s of antiferrodistortive rotation are converted from d t z-s.The obtained coefficients c t is and oxygen displacements d t is and oxygen octahedral rotation angles θ t z are summarized in Supplementary Tables 1 and 2, respectively.Note that for all the invested thickness (t = 2, 4, 6, and 8 u.c.), the remaining term (Φ t rem) mainly come from the atomic displacements on the surface layer (Supplementary Fig. 15), and the displacements of atoms near the LaSr dopants (Supplementary Fig. 3).These surface atomic displacements result in a downward atomic rumpling on the 0 th TiO2 sublayer (top surface) and an upward atomic rumpling on the -0.5 th (La, Sr)O layer.This DFT calculated rumpling behavior of the LSTO film surface is also reported in undoped TiO2-terminated STO (001) surface (see Supplementary Note 9).
This slab structure also shows the periodic charge modulation of Ti 3+ O6 and Ti 4+ O6 with the expanded and contracted TiO6 octahedra and exhibits the antiferromagnetic Mott insulating behavior with the localized d band when t ≤ 6 u.c.(Fig. 4d, Supplementary Fig. 17c,f), indicating CO phase.Note that the obtained atomic and electronic structures of the LSTO/STO slab have similar characteristics to those of the CO phase in the bulk LSTO.Thus, we conclude that the metastable CO phase of bulk LSTO is stabilized in the LSTO/STO heterostructure (Fig. 4e).
When t = 8 u.c., the layer-resolved density of state (LDOS) shows the metallic state with the occupied conduction bands on the -8 th and -9 th layers, which is in the STO substrate (Supplementary Fig. 18).This indicates that the electrons originating from LaSr dopants, which are located on the -6.5 th and -7.5 th sublayer, were transferred to the STO substrate due to the formation of LSTO/STO junctions 13 .The carrier spreading can evoke a metallic response from a substrate even when the substrate was insulating.Since ionized impurity scattering center such as LaSr dopant does not exist in STO substrate, these electrons can exhibit high mobility at low temperatures, resulting in an extremely large residual resistivity ratio (RRR) (Fig. 2d).
It has been reported that low temperature electron mobility of LSTO thin films increased with the decrease in La-doping concentration, leading to a large RRR 14 .Therefore, we attribute that the large RRR of the 8 u.c.thick LSTO thin film originates from substrate conduction.
We would like to note that the calculated electronic structure of each layer might not perfectly match the experimental situation, since the LaSr dopants in the calculation are regularly distributed unlike in the real sample case.However, the underlying physics of the surface-induced OSMT, the stabilization of the CO phase, and subsequent MIT are irrelevant to the doping distribution.rule 19,20 , an equilibrium cation-anion bond length strongly depends on the coordination number.
Due to the decreased coordination number of the Ti and O atoms (TiO6 octahedra to TiO5 pyramid and Sr4Ti2O octahedra to Sr2Ti2O polyhedra) on the TiO2 terminated SrTiO3 surface, shortened Ti-O and Sr-O equilibrium bond lengths result in downward and upward rumpling on the 0 th TiO2 sublayer (top surface) and -0.5 th SrO sublayer, respectively 21 .Note that these surface atomic rumpling in the TiO2 terminated LSTO film is well described in our DFT calculations (Supplementary Fig. 20).
To confirm this atomic rumpling behavior experimentally, we carried out synchrotron surface X-ray diffraction measurements and performed COBRA analysis of an LSTO thin film (t = 8 u.c.).The complete atomic structures of each unit cell of the LSTO thin film including the surface unit cell in focus can be obtained from COBRA analysis.Supplementary Figure 20 shows the COBRA derived full electron density map with 2D vertical slices on the (110) atomic  001) surface after the annealing process.The STO substrate was etched 45 sec using buffered-HF and annealed at 1100 °C for 6 hours.Before the film growth, the second chemical etching procedure using buffered-HF for 10 sec was performed to stabilize the TiO2-terminated surface of the STO substrates 18 .b RHEED pattern of the LSTO thin film surface after growth.The LSTO thin film is grown under 10 -5 Torr of oxygen/ozone mixture and at 650 °C.
On the other hand, we found that the CO along the in-plane direction strongly depends on La-doping concentration.In 25% La-doped STO, Ti 3+ /Ti 4+ ionic ordering has an in-plane checkerboard arrangement (Supplementary Fig. 24b), while, in 12.5% La-doped STO, Ti 3+ /Ti 4+ ionic ordering along the in-plane direction depends on the site configuration of LaSr.By evaluating the stability of the several different configurations for the Ti 3+ /Ti 4+ ionic ordering arrangement along the in-plane direction, we found that the electrons originated from LaSr tends to be localized at the nearest neighbor Ti sites of LaSr (Supplementary Fig. 24c).This implies that the formation of diagonal rows of Ti 3+ /Ti 4+ ionic ordering is accompanied by LaSr.
We expect that such an ordering of Ti 3+ /Ti 4+ with LaSr is a primary building block for the charge-ordered phase in the La-doped STO system.The lattice periodicity along the [110]   or the [110] direction for the ordering of Ti 3+ /Ti 4+ with LaSr may depend on the La-doping concentration.In fact, similar types of charge-ordered stripes have been reported in commensurate 25 and incommensurate 26 carrier-doped manganite.The diagonal Mn 3+ stripes are separated by the regions of Mn 4+ ions and create a periodic array, that is charge-ordered phase 25 .The spacing between diagonal Mn 3+ stripes is inversely proportional to the doping concentration.Therefore, we attribute that the CO phase is not limited to specific doping concentrations but can exist within a certain range of doping concentrations in the LaxSr1-xTiO3 system.We believe that these subjects will be an intriguing area for the future research.
7 -5.5 eV, respectively.The complex dielectric functions, () [≡ 1 +  4   ̃()], were estimated with a three-phase model composed of one Drude component and two Lorentz oscillators.The two Lorentz oscillators, located at 1.5 eV and 3.4 eV, correspond to the incoherent mode and the charge transfer excitation, respectively.The dielectric function yielded from the three-phase model fitting was checked by point-bypoint fitting.The two dielectric functions, extracted by different fitting methods, were consistent with each other.The optical data were also confirmed by comparing a reflectivity directly measured by the conventional FT-IR/grating-type spectrometers in a photon energy range of 0.1 eV -5.5 eV.The reflectivity taken from the direct measurement was in accordance with the resistivity extracted from the ellipsometry.

Supplementary Fig. 13 |
DFT calculated spin-polarized band structure of the LSTO/STO slab.Spin-polarized band structures of the LSTO films on STO with various film thickness t = 2, 4, 6 and 8 u.c.. a 2 u.c., b 4 u.c., c 6 u.c. and d 8 u.c..The bands are projected to minimize spurious electronic states originating from the fixed bottom surface layer of the slab, where the STO 2 u.c.from the bottom surface are excluded from the projection.Burgundy and indigo colors represent the spin-up and spin-down bands, respectively.For t = 2, 4, 6 u.c., the midpoint of the energies of the lowest unoccupied state and the highest occupied state is set to be zero and represented by the horizontal lines.For t = 8 u.c., the Fermi energy is set to be zero and represented by the horizontal lines.
plane and (200) atomic plane, respectively.The slices along the (200) atomic plane cuts through the Ti, apical oxygen, and equatorial oxygen sites.Therefore, we can quantitatively determine the Ti-O atomic rumpling (δTi-O) magnitude.Likewise, we identify (La, Sr)-O atomic rumpling (δ(La, Sr)-O) magnitude using the slice along the (110) atomic plane cutting through the (La, Sr), and apical oxygen sites.The slice along the (200) and (110) atomic planes reveal a downward rumpling on the 0 th TiO2 sublayer (top surface) and upward rumpling on the -0.5 th (La, Sr)O sublayer.Therefore, we conclude that experimentally determined surface structures such as atomic rumpling behavior at the surface layer are in good agreement with those obtained from the DFT calculations.Supplementary Fig. 19 | RHEED patterns for LSTO thin film growth obtained at room temperature along the [100] azimuths.a RHEED pattern of the STO (